CN107221012A - Static PET image reconstruction method based on the Kalman filtering for improving the scope of application - Google Patents
Static PET image reconstruction method based on the Kalman filtering for improving the scope of application Download PDFInfo
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- G06T11/003—Reconstruction from projections, e.g. tomography
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Abstract
A kind of static PET image reconstruction method based on the Kalman filtering for improving the scope of application, including (1) obtain the observation data of system, set up the state-space model of PET system by data acquisition and correction；(2) spatial concentration distribution of radioactive substance is reconstructed based on state space filtering method；Static PET image reconstruction is carried out based on the Kalman filtering for improving the scope of application.Null matrix is expressed as by the method inverted the invention provides a kind of radioactive substance spatial concentration predictor error covariance matrix for tending to infinity that can not store script, then offline, iterative calculation radioactive substance spatial concentration predictor error covariance matrix inverse matrix, and filtering gain is calculated based on inverse matrix, the method for finally providing the reconstruction of radioactive substance spatial concentration reconstructed results.
Description
Technical field
The present invention relates to positron emission tomography field, and in particular to a kind of based on improving the scope of application
The static PET image reconstruction method of Kalman filtering.
Background technology
Positron emission tomography (Positron Emission Tomography, PET) is a kind of based on nuclear physics
, the Medical Imaging Technology of molecular biology, different from CT imagings, PET can detect life as a kind of functional imaging technology
Metabolic situation in object, and the physiology of reflection organism or pathological change on a molecular scale, can be early stage disease
Detection provides effective foundation with prevention, has been widely used in the diagnosis of tumour, heart disease, nerve and psychosis
And drug screening and exploitation, with huge application prospect.
Positron nuclide is produced first by medical cyclotron when carrying out PET scan, then will be marked
Radioactivity is with the tracer injection organism of position nucleic, and by blood circulation, tracer can be in each histoorgan of organism
Form certain concentration distribution.Radioactivity is extremely unstable with position nucleic, it may occur that decay.In decay process, the same position of radioactivity
Nucleic can produce positive electron and occur annihilation reaction with the free electron in histoorgan surrounding environment, produce a pair of almost directions
Conversely, the equal gamma photons of energy.PET scan can catch these photons and then generate data for projection.Based on these projections
Data and restructing algorithm, can reconstruct the concentration distribution of radioactive substance in histoorgan.But due to being collected via PET scan
Data for projection in contain substantial amounts of noise information, this will influence the quality of PET image reconstruction, so the weight of PET image
It is the big focus of one studied now to build algorithm.
At present, PET image reconstruction method is broadly divided into two classes：Analytic method, iterative method.Previous class is main instead to be thrown with filtering
Shadow method is representative, and calculating speed is fast, and cost is small, but can not suppress noise well, so that artifact is serious, reconstructed image quality
It is not high.Therefore, the Statistics Iteration using more typical ML-EM as representative is occurred in that.Statistics Iteration is suitable to fragmentary data
Answering property is good, and the reconstruction image of acquisition becomes apparent from than analytic method, is quickly become the focus of PET algorithm for reconstructing research.State space
The introducing of observation model so that based on Kalman filtering, H∞The algorithm for estimating such as filtering are rebuild PET image and are possibly realized.Although such as
This, because statistical property, checking inertia condition that data for projection is not used are difficult, based on H∞The PET reconstruction results of filtering have
Reconstruction result is conservative, it is computationally intensive the problems such as；Due to can not store within a processor, filtered based on standard Kalman
Reconstructing method can not (i.e. the initial of radioactive substance concentration be estimated suitable for not being sure completely to the estimation of initial activity material concentration
Count error covariance matrix infinitely great) situation.
The content of the invention
In order to overcome existing PET image reconstruction method can not be applied to initial activity material concentration estimation do not have completely
The narrower deficiency of situation, the scope of application of assurance, effective the suitable based on improving of the scope of application is expanded the invention provides a kind of
With the static PET image reconstruction method of the Kalman filtering of scope, the invention tends to be infinitely great by what script can not be stored first
The initial predictor error covariance matrix of radioactive substance spatial concentration be stored as null matrix in its inverse form, then by from
Line, the inverse matrix for iterating to calculate predictor error covariance matrix, and then filtering gain is calculated based on inverse matrix, it finally ensure that reconstruct
Process is smoothed out.
In order to solve the above-mentioned technical problem the present invention provides following technical scheme：
A kind of static PET image reconstruction method based on the Kalman filtering for improving the scope of application, comprises the following steps：
(1) by data acquisition and correction, the observation data of system is obtained, the state-space model of PET system is set up：
Wherein, t represents the time；xtFor need rebuild object t radioactive substance spatial concentration distribution；yt
It is the sinogram data obtained after noise is corrected for the observation of t；HtRepresent the space of human body inside radiation material
The projection matrix of projection relation between concentration and sinogram data；vtIt is t data acquisition and is remained after being corrected through noise
Noise, vtIt is 0 to obey average, and variance is R normal distribution；
(2) reconstruction image based on the Kalman filtering for improving the scope of application is obtained according to following equations：
Wherein,For the initial estimate of the spatial concentration of radioactive substance, M is that the space of initial activity material is dense
The inverse matrix of the predictor error covariance matrix of degree, ItFor the predictor error covariance matrix of the spatial concentration of t radioactive substance
Inverse matrix, KtIt is the filtering gain matrix of t,For the estimate of the spatial concentration of the radioactive substance of t, iteration
From initial valueI0Set out, with reference to observation yt, by t iteration, obtain the spatial concentration distribution of final radioactive substance
Estimate
Further, in the step (2), reconstruction iteration process is as follows：
2.1) initial value of the spatial concentration distribution of setting radioactive substance and the space of initial activity material first is dense
Spend the inverse matrix of predictor error covariance matrixI0；
2.2) the predictor error covariance matrix of the spatial concentration of the radioactive substance of t is calculated using equation (1.4)
Inverse matrix It；
2.3) using t radioactive substance spatial concentration the inverse matrix I for estimating covariance matrixtAccording to equation
(1.3) the filtering gain matrix K of t is calculatedt；
2.4) the spatial concentration estimate of t-1 moment radioactive substances is utilizedT is calculated according to equation (1.2)
The spatial concentration estimate of radioactive substance
2.5) repeat step 2.2), 2.3), 2.4) until obtaining the final reconstructed results for meeting and requiring
2.6) according to step 2.5) obtain final radioactive substance spatial concentration distribution estimate
The present invention technical concept be：Based on the analysis for using PET system standard Kalman filtering method image-forming principle,
It was found that the reconstructing method can not be applied to (i.e. initial activity material of not being sure completely to initial radioactive substance concentration distribution
The evaluated error covariance matrix of concentration distribution is infinitely great) situation.The invention tends to be infinitely great by what script can not be stored first
The initial predictor error covariance matrix of radioactive substance spatial concentration be stored as null matrix in its inverse form, then by from
Line, the inverse matrix for iterating to calculate predictor error covariance matrix, and then filtering gain is calculated based on inverse matrix, it finally ensure that reconstruct
Process is smoothed out.
It can be seen from the above technical proposal that beneficial effects of the present invention are mainly manifested in：Introduce radioactive substance concentration
Originally infinitely great image predictor error covariance matrix can be converted into null matrix and carried out by the inverse matrix of predictor error covariance matrix
Storage, thus expand the scope of application of the static PET image reconstructing method based on Kalman filtering.
Brief description of the drawings
Fig. 1 is the step schematic flow sheet of PET image reconstruction method of the present invention.
Embodiment
In order to more specifically describe the present invention, below in conjunction with the accompanying drawings and embodiment to the present invention static PET
Concentration reestablishing method is described in detail.
As shown in figure 1, a kind of static PET image reconstruction method based on the Kalman filtering for improving the scope of application, bag
Include following steps：
(1), by data acquisition and correction, the observation data of system are obtained, the state-space model of PET system is set up；：
Wherein, t represents the time；xtThe spatial concentration distribution of the radioactive substance for the object t rebuild for needs；ytFor t
The observation at moment, is the sinogram data obtained after noise is corrected；HtRepresent that the space of human body inside radiation material is dense
The projection matrix of projection relation between degree and sinogram data；vtIt is t data acquisition and making an uproar of being remained after being corrected through noise
Sound, vtIt is 0 to obey average, and variance is R normal distribution.
(2) the static PET reconstruction images based on the Kalman filtering for improving the scope of application are obtained according to following equations：
Wherein,For the initial estimate of the spatial concentration of radioactive substance, M is that the space of initial activity material is dense
The inverse matrix of the predictor error covariance matrix of degree, ItFor the predictor error covariance matrix of the spatial concentration of t radioactive substance
Inverse matrix, KtIt is the filtering gain matrix of t,For the estimate of the spatial concentration of the radioactive substance of t, iteration
From initial valueI0Set out, with reference to observation yt, by t iteration, obtain the spatial concentration distribution of final radioactive substance
Estimate
As shown in figure 1, the image reconstruction iterative process based on the Kalman filtering for improving the scope of application is as follows：
2.1) initial value of the spatial concentration distribution of setting radioactive substance and the space of initial activity material first is dense
Spend the inverse matrix of predictor error covariance matrixI0；
2.2) the predictor error covariance matrix of the spatial concentration of the radioactive substance of t is calculated using equation (1.4)
Inverse matrix It；
2.3) using t radioactive substance spatial concentration the inverse matrix I for estimating covariance matrixtAccording to equation
(1.3) the filtering gain matrix K of t is calculatedt；
2.4) the spatial concentration estimate of t-1 moment radioactive substances is utilizedT is calculated according to equation (1.2)
The spatial concentration estimate of radioactive substance
2.5) repeat step 2.2), 2.3), 2.4) until obtaining the final reconstructed results for meeting and requiring
2.6) according to step 2.5) obtain final radioactive substance spatial concentration distribution estimate
Claims (2)
1. a kind of static PET image reconstruction method based on the Kalman filtering for improving the scope of application, it is characterised in that：Including
Following steps：
(1) by data acquisition and correction, the observation data of system is obtained, the state-space model of PET system is set up；
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Wherein, t represents the time；xtThe spatial concentration distribution of the radioactive substance for the object t rebuild for needs；ytFor t
Observation, the sinogram data exactly obtained after noise is corrected；HtRepresent the spatial concentration of human body inside radiation material
The projection matrix of projection relation between the numerical value obtained with PET scan；vtIt is t data acquisition and residual after being corrected through noise
The noise stayed, vtIt is 0 to obey average, and variance is R normal distribution；
(2) spatial concentration distribution of radioactive substance is reconstructed based on state space filtering method；
Obtained according to following equations based on the static PET image reconstruction result of the Kalman filtering for improving the scope of application：
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Wherein,For the initial estimate of the spatial concentration of radioactive substance, M is the spatial concentration of initial activity material
The inverse matrix of predictor error covariance matrix, ItFor the spatial concentration of t radioactive substance predictor error covariance matrix it is inverse
Matrix, KtIt is the filtering gain matrix of t,For the estimate of the spatial concentration of the radioactive substance of t, iteration is from first
Initial valueI0Set out, with reference to observation yt, by t iteration, the spatial concentration distribution for obtaining final radioactive substance is estimated
Evaluation
2. the static PET image reconstruction method as claimed in claim 1 based on the Kalman filtering for improving the scope of application, its
It is characterised by：In the step (2), reconstruction iteration process is as follows：
2.1) initial value of the spatial concentration distribution of setting radioactive substance and the spatial concentration of initial activity material first is pre-
Estimate the inverse matrix of error covariance matrixI0；
2.2) the inverse square of the predictor error covariance matrix of the spatial concentration of the radioactive substance of t is calculated using equation (1.4)
Battle array It；
2.3) using t radioactive substance spatial concentration the inverse matrix I for estimating covariance matrixtCounted according to equation (1.3)
Calculate the filtering gain matrix K of tt；
2.4) the spatial concentration estimate of t-1 moment radioactive substances is utilizedThe radiation of t is calculated according to equation (1.2)
The spatial concentration estimate of property material
2.5) repeat step 2.2), 2.3), 2.4) until obtaining the final reconstructed results for meeting and requiring
2.6) according to step 2.5) obtain final radioactive substance spatial concentration distribution estimate
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2017
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